Answer:
C
Step-by-step explanation:
So, we want to find the equation of the line graphed.
To do so, let's first find the slope. Let's pick two points from the graph. I'm going to use (-2,2) and (0,-1).
The formula for slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let's let (-2, 2) be (x₁, y₁) and let's let (0,-1) be (x₂, y₂). So, substitute:
[tex]m=\frac{-1-2}{0-(-2)}[/tex]
Subtract:
[tex]m=\frac{-3}{2}[/tex]
So, our slope is -3/2.
Now, we can use the point-slope form, which is:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is any point on the graph.
Since our answer choices are using the values 2 and 4, this means we can use the point (2,-4).
So, (2,-4) is our (x₁, y₁).
Also, our m is -3/2. So, substitute these into the point-slope form:
[tex]y-(-4)=-\frac{3}{2}(x-2)[/tex]
Simplify:
[tex]y+4=-\frac{3}{2}(x-2)[/tex]
Therefore, our answer is C.
And we're done!
